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Calculators › Cylindrical Gear Design
Gear Design Suite

Cylindrical Gear Design Calculator

Complete design verification suite for spur and helical cylindrical gears per GB/T 3480. Seven modules covering geometry calculation, transmission parameter checks, contact fatigue strength, bending fatigue strength, and backlash inspection.

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cylindrical-gear-design
Core Formulas (7 modules):
M3 Geometry:
d1 = m · z1 / cos(β) a = (d1 + d2) / 2 εγ = εα + εβ
M5 Contact Fatigue:
σH = ZH · ZE · Zε · Zβ · √(KA·Ft·(u+1)·Kv·KHβ·KHα / (b·d1·u))
M6 Bending Fatigue:
σF = KA · Ft · Kv · KFβ · KFα · YFS · Yε · Yβ / (b · m)
M7 Backlash:
Wn = cos(α) · [π·(k-0.5) + z·inv(α)] · m
Judgment: σH ≤ σHP and σF ≤ σFP for both pinion and gear → PASS

Why This Calculator

7-Module Suite

Geometry, parameter checks, contact fatigue, bending fatigue, and backlash inspection — all in one comprehensive calculator.

GB/T 3480 Standard

Calculations follow the Chinese national standard for cylindrical gear load capacity verification.

49 Material Library

Built-in material database with σHlim, σFlim, and heat-treatment-dependent properties.

YFS Bilinear Interp

Tooth form factor YFS computed via 18×29 bilinear interpolation table, no manual lookup.

inv(α) Newton Solver

Involute function inv(α) = tan(α) − α solved via Newton iteration, no lookup table needed.

Auto Pass/Fail

Instant judgment on contact and bending stress against allowable limits for pinion and gear.

How It Works

Enter Parameters

Input power P, pinion speed n1, gear ratio u, mesh type, materials, quality grade, precision grade, reliability.

Compute Geometry

Calculate z1, z2, m, β, d1, d2, center distance a, addendum/dedendum, contact ratios εα/εβ/εγ.

Verify Strength

Compute contact stress σH and bending stress σF, compare with allowable σHP/σFP.

Inspect Backlash

Calculate span measurement teeth k, common normal length Wn, chord tooth height/thickness for manufacturing.

Who Is It For

Gear Design Engineers | Mechanical Engineers | Manufacturing Inspectors | R&D Engineers

Key Highlights

GB/T 34807 Modules49 MaterialsYFS InterpolationNewton SolverAuto Judgment

Ready to Calculate?

Enter your design parameters and get instant verification across all 7 modules.

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